Abstract
In this paper we present the SteinLib, a library of data sets for the Steiner tree problem in graphs. This library extends former libraries on Steiner tree problems by many new interesting and difficult instances, most of them arising from real-world applications. We give a survey on the difficulty of these problem instances by stating references to state-of-the-art software packages that were the first or are currently among the best to solve these instances.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Y.P. Aneja. An integer linear programming approach to the Steiner problem in graphs. Networks,10:167–178, 1980.
J.E. Beasley. An algorithm for the Steiner problem in graphs. Networks, 14:147–159, 1984.
J.E. Beasley. An SST-based algorithm for the Steiner problem in graphs. Networks, 19:1–16, 1989.
J.E. Beasley. OR-Library: Distributing test problems by electronic mail. Journal of the Operational Research Society, 41:1069–1072, 1990.
J.E. Beasley. A heuristic for Euclidean and rectilinear Steiner problems. European Journal of Operational Research, 58:284–292, 1992.
R.E. Bixby, S. Celia, C. McZeal, and M.W.P. Savelsbergh. An updated mixed integer programming library: MIPLIB 3.0. Paper and Problems available at WWW Page: URL http://www.caam.rice.edu/~bixby/miplib/miplib.html, 1998.
R. Borndörfer. Aspects of Set Packing, Partitioning, and Covering. PhD thesis, Technische Universität Berlin, 1998.
S.A. Canuto, C.C. Ribeiro, and M.G.C. Resende. Local search with perturbations for the prize collecting Steiner tree problem. In Extended Abstracts of the third Metaheuristics International Conference, pages 115–119. Catholic University of Rio de Janeiro, 1999.
J. Cho and J. Breen. Analysis of the performance of dynamic multicast routing algorithms. Computer Communications, 22:667–674, 1999.
S. Chopra, E.R. Gorres, and M.R. Rao. Solving the Steiner tree problem on a graph using branch and cut. ORSA Journal on Computing, 4:320–335, 1992.
K.A. Dowsland. Hill-climbing, simulated annealing and the Steiner problem in graphs. Engineering Optimization, 17:91--107, 1991.
D.-Z. Du, J.M. Smith, and J.H. Rubinstein, editors. Advances in Steiner Trees. Kluwer, Boston, 2000.
C. Duin. Steiner Problems in Graphs. PhD thesis, University of Amsterdam, 1993.
C. Duin. Preprocessing the Steiner problem in graphs. In D.-Z. Du, J.M. Smith, and J.H. Rubinstein, editors, Advances in Steiner Trees, pages 175–233. Kluwer, 2000.
C. Duin and A. Volgenant. An edge elimination test for the Steiner problem in graphs. Operations Research Letters, 8:79–83, 1989.
C. Duin and A. Volgenant. Reduction tests for the Steiner problem in graphs. Networks, 19:549–567, 1989.
C. Duin and S. Voß. Steiner tree heuristics — a survey. In H. Dyckhoff, U. Derigs, M. Salomon, and H. C. Tijms, editors, Operations Research Proceedings, pages 485–496, Berlin, 1994. Springer.
C. Duin and S. Voß. Efficient path and vertex exchange in Steiner tree algorithms. Networks,29:89–105, 1997.
C. Duin and S. Voß. The Pilot method: A strategy for heuristic repetition with application to the Steiner problem in graphs. Networks,34:181–191, 1999.
R.E. Erickson, C.L. Monma, and A.F. Veinott. Send-and-split method for minimum concave-cost network flows. Mathematics of Operations Research, 12:634–664, 1987.
J.S. Farris. Inferring phylogenetic trees from chromosome inversion data. Systematic Zoology, 27:275–284, 1987.
C.E. Ferreira. O problema de Steiner em grafos: urna abordagem Poliédrica. Master’s thesis, Universidade de São Paulo, 1989.
A. Ghanwani. Neural and delay based heuristics for the Steiner problem in networks. European Journal of Operational Research, pages 241–265, 1998.
M.X. Goemans and Y.-S. Myung. A catalog of Steiner tree formulations. Networks, 23:19–28, 1993.
L. Gouveia. Using variable redefinition for computing minimum spanning and Steiner trees with hop constraints. Technical report, Faculdade de Ciencias, Universidade de Lisboa, 1997.
M. Grötschel, A. Martin, and R. Weismantel. The Steiner tree packing problem in VLSI-design. Mathematical Programming, 78:265–281, 1997.
M. Hanan. On Steiner’s problem with rectilinear distance. SIAM Journal of Applied Mathematics, 14:255–265, 1966.
F.K. Hwang, D.S. Richards, and P. Winter. The Steiner tree problem. Annals of Discrete Mathematics, 53, 1992.
E. Ihler, G. Reich, and P. Widmayer. Class Steiner trees and VLSI-design. Discrete Applied Mathematics, 90:173–194, 1999.
D.S. Johnson, M. Minkoff, and S. Phillips. The prize collecting Steiner tree problem: theory and practice. In Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms, pages 760–769. SIAM, 2000.
J.J. Johnston, R.I. Kelley, T.O. Crawford, D.H. Morton, R. Agarwala, T. Koch, A.A. Schäffer, C.A. Francomano, and L.G. Biesecker. A novel nemaline myopathy in the Amish caused by a mutation in troponin T1. American Journal of Human Genetics, pages 814–821, October 2000.
M. Jünger, A. Martin, G. Reinelt, and R. Weismantel. Quadratic 0/1 optimization and a decomposition approach for the placement of electronic circuits. Mathematical Programming, 63:257–279, 1994.
B.N. Khoury and P.M. Pardalos. A heuristic for the Steiner problem in graphs. Computational Optimization and Applications, 6:5–14, 1996.
B.N. Khoury, P.M. Pardalos, and D.-Z. Du. A test problem generator for the Steiner problem in graphs. ACM Transactions on Mathematical Software, 19:509–522, 1993.
T. Koch and A. Martin. Solving Steiner tree problems in graphs to optimality. Networks, 32:207–232, 1998.
T. Koch, A. Martin, and M. Zachariasen. Computations based on [35] and [66], 1999.
M. Körkel. Effiziente Verfahren zur Lösung unkapazitierter Standort-Probleme. vwf, Berlin, 1999.
B. Korte, H.J. Prömel, and A. Steger. Steiner trees in VLSI-layout. In B. Korte, L. Lovász, H.J. Prömel, and A. Schrijver, editors, Paths, Flows, and VLSI-Layout, pages 185–214. Springer, Berlin, 1990.
D. Lee. Some industrial case studies of Steiner trees. Paper presented at the NATO Advanced Research Workshop Topological Network Design Analysis and Synthesis, Copenhagen, 1989.
T. Lengauer. Combinatorial Algorithms for Integrated Circuit Layout. Wiley, New York, 1990.
A. Lin. Personal communication, 2001.
C.P. Low. Loop-free multicast routing with end-to-end delay constraints. Computer Communications, 22:181–192, 1999.
A. Lucena. Steiner problem in graphs: Lagrangean relaxation and cutting-planes. Bulletin of the Committee on Algorithms, 21:2–7, 1992.
A. Lucena and J.E. Beasley. A branch and cut algorithm for the Steiner problem in graphs. Networks, 31:39–59, 1998.
F. Margot. Personal communication, 1994.
M. Minoux. Efficient greedy heuristics for Steiner tree problems using reoptimization and supermodularity. INFOR,28:221–233, 1990.
Y.-S. Myung, C.-H. Lee, and D.-W. Tcha. On the generalized minimum spanning tree problem. Networks, 26:231–242, 1995.
D. Penny and M.D. Hendy. Turbotree: A fast algorithm for minimal trees. Computer Applications in the Biosciences, 3:183–187, 1987.
J. Plesnik. The Steiner tree problem in graphs: Worst case examples for insertion heuristics. International Journal of Mathematical Algorithms, 1:21–34, 1999.
T. Polzin and S.V. Daneshmand. Improved algorithms for the Steiner problem in networks. Technical report, University of Mannheim, 1998.
V.J. Rayward-Smith and A. Clare. On finding Steiner vertices. Networks,16:283–294, 1986.
G. Reinelt. TSPLIB — a traveling salesman problem library. ORSA Journal on Computing,3:376–384, 1991.
J. Sessions. Solving for habitat connections as a Steiner network problem. Forest Science, 38:203–207, 1992.
J. Soukup and W.F. Chow. Set of test problems for the minimum length connection networks. ACM/SIGMAP Newsletters, 15:48–51, 1973.
C. Stanton and J. MacGregor Smith. Steiner trees and 3d macromolecular conformation. Technical report, University of Massachusets, Amherst, 2000.
E. Uchoa, M.P. de Aragão, and C. Ribeiro. Preprocessing Steiner problems from visi layout. Technical Report MCC 32/99, PUC-Rio, 1999.
M.G.A. Verhoeven. Parallel Local Search. PhD thesis, Eindhoven University of Technology, 1996.
M.G.A. Verhoeven, M.E.M. Severens, and E.H.L. Aarts. Local search for Steiner trees in graphs. In V.J. Rayward-Smith, I.H. Osman, C.R. Reeves, and G.D. Smith, editors, Modern Heuristic Search Methods, pages 117–129. Wiley, Chichester, 1996.
S. Voß. Steiner-Probleme in Graphen. Hain, Frankfurt/Main, 1990.
S. Voß. Steiner’s problem in graphs: Heuristic methods. Discrete Applied Mathematics, 40:45–72, 1992.
S. Voß. Observing logical interdependencies in tabu search — methods and results. In V.J. Rayward-Smith, I.H. Osman, C.R. Reeves, and G.D. Smith, editors, Modern Heuristic Search Methods, pages 41–59. Wiley, Chichester, 1996.
S. Voß. The Steiner tree problem with hop constraints. Annals of Operations Research, 86:321–345, 1999.
S. Voß. Modern heuristic search methods for the Steiner tree problem in graphs. In D.-Z. Du, J.M. Smith, and J.H. Rubinstein, editors, Advances in Steiner Trees, pages 283–323. Kluwer, 2000.
J.A. Wald and P.G. Sorensen. Resolving the query inference problem using Steiner trees. ACM Transactions on Database Systems, 9:348–368, 1984.
G.A. Walters. The design of the optimal layout for a sewer network. Engineering Optimization, 9:37–50, 1985.
D.M. Warme, P. Winter, and M. Zachariasen. Exact algorithms for plane Steiner tree problems: A computational study. In D.-Z. Du, J. M. Smith, and J. H. Rubinstein, editors, Advances in Steiner Trees, pages 81–116. Kluwer, 2000.
D.M. Warme and M. Zachariasen. Personal communication, 2000.
B.M. Waxman. Routing of multipoint connections. IEEE Journal on Selected Areas in Communications, 6:1617–1622, 1988.
P. Winter. Steiner problem in Halin networks. Discrete Applied Mathematics, 17:281–294, 1987.
P. Winter. Reductions for the rectilinear Steiner tree problem. Technical Report 11–95, Rutcors University, 1995.
P. Winter and J.M. Smith. Path-distance heuristics for the Steiner problem in undirected networks. Algorithmica, 7:309–327, 1992.
R.T. Wong. A dual ascent approach for the Steiner tree problems on a directed graph. Mathematical Programming, 28:271–287, 1984.
J. Xu, S.Y. Chiu, and F. Glover. A probabilistic tabu search for the telecommunications network design. Combinatorial Optimization: Theory and Practice, 1:69–94, 1996.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Kluwer Academic Publishers
About this chapter
Cite this chapter
Koch, T., Martin, A., Voß, S. (2001). SteinLib: An Updated Library on Steiner Tree Problems in Graphs. In: Cheng, X.Z., Du, DZ. (eds) Steiner Trees in Industry. Combinatorial Optimization, vol 11. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0255-1_9
Download citation
DOI: https://doi.org/10.1007/978-1-4613-0255-1_9
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7963-8
Online ISBN: 978-1-4613-0255-1
eBook Packages: Springer Book Archive